# Properties

 Label 1428.2 Level 1428 Weight 2 Dimension 22720 Nonzero newspaces 40 Sturm bound 221184 Trace bound 15

## Defining parameters

 Level: $$N$$ = $$1428 = 2^{2} \cdot 3 \cdot 7 \cdot 17$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$40$$ Sturm bound: $$221184$$ Trace bound: $$15$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(1428))$$.

Total New Old
Modular forms 57216 23328 33888
Cusp forms 53377 22720 30657
Eisenstein series 3839 608 3231

## Trace form

 $$22720 q - 2 q^{3} - 52 q^{4} - 12 q^{5} - 20 q^{6} - 16 q^{7} + 12 q^{8} - 42 q^{9} + O(q^{10})$$ $$22720 q - 2 q^{3} - 52 q^{4} - 12 q^{5} - 20 q^{6} - 16 q^{7} + 12 q^{8} - 42 q^{9} - 16 q^{10} - 20 q^{11} + 4 q^{12} - 92 q^{13} + 48 q^{14} - 12 q^{15} + 28 q^{16} - 20 q^{17} - 28 q^{18} - 34 q^{21} - 184 q^{22} - 8 q^{23} - 12 q^{24} + 4 q^{25} + 68 q^{26} + 4 q^{27} - 68 q^{28} + 152 q^{29} + 36 q^{30} + 136 q^{31} + 100 q^{32} + 26 q^{33} + 168 q^{34} + 52 q^{35} - 108 q^{36} + 28 q^{37} + 124 q^{38} + 20 q^{39} + 144 q^{40} + 32 q^{41} - 88 q^{42} + 16 q^{43} + 80 q^{44} - 62 q^{45} - 48 q^{46} - 36 q^{47} - 188 q^{48} - 196 q^{49} - 84 q^{50} + 43 q^{51} - 176 q^{52} - 208 q^{54} + 64 q^{55} - 116 q^{56} + 116 q^{57} - 288 q^{58} + 88 q^{59} - 264 q^{60} + 144 q^{61} - 224 q^{62} + 106 q^{63} - 268 q^{64} + 444 q^{65} - 236 q^{66} + 184 q^{67} - 316 q^{68} + 56 q^{69} - 80 q^{70} - 180 q^{72} + 260 q^{73} - 60 q^{74} + 12 q^{75} - 120 q^{76} + 32 q^{77} - 48 q^{78} - 40 q^{79} - 80 q^{80} - 34 q^{81} - 56 q^{82} - 8 q^{83} + 116 q^{84} - 428 q^{85} + 132 q^{86} - 216 q^{87} + 176 q^{88} - 120 q^{89} - 112 q^{90} - 136 q^{91} + 168 q^{92} - 266 q^{93} - 16 q^{94} - 92 q^{95} - 204 q^{96} - 368 q^{97} + 84 q^{98} - 4 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(1428))$$

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space $$S_k^{\mathrm{new}}(N, \chi)$$ we list the newforms together with their dimension.

Label $$\chi$$ Newforms Dimension $$\chi$$ degree
1428.2.a $$\chi_{1428}(1, \cdot)$$ 1428.2.a.a 1 1
1428.2.a.b 1
1428.2.a.c 1
1428.2.a.d 1
1428.2.a.e 1
1428.2.a.f 2
1428.2.a.g 2
1428.2.a.h 2
1428.2.a.i 2
1428.2.a.j 3
1428.2.c $$\chi_{1428}(307, \cdot)$$ n/a 128 1
1428.2.d $$\chi_{1428}(169, \cdot)$$ 1428.2.d.a 2 1
1428.2.d.b 6
1428.2.d.c 12
1428.2.g $$\chi_{1428}(713, \cdot)$$ 1428.2.g.a 48 1
1428.2.h $$\chi_{1428}(239, \cdot)$$ n/a 192 1
1428.2.j $$\chi_{1428}(545, \cdot)$$ 1428.2.j.a 22 1
1428.2.j.b 22
1428.2.m $$\chi_{1428}(407, \cdot)$$ n/a 216 1
1428.2.n $$\chi_{1428}(475, \cdot)$$ n/a 144 1
1428.2.q $$\chi_{1428}(205, \cdot)$$ 1428.2.q.a 2 2
1428.2.q.b 2
1428.2.q.c 2
1428.2.q.d 2
1428.2.q.e 8
1428.2.q.f 8
1428.2.q.g 8
1428.2.q.h 12
1428.2.s $$\chi_{1428}(55, \cdot)$$ n/a 288 2
1428.2.u $$\chi_{1428}(293, \cdot)$$ 1428.2.u.a 96 2
1428.2.w $$\chi_{1428}(421, \cdot)$$ 1428.2.w.a 4 2
1428.2.w.b 16
1428.2.w.c 20
1428.2.y $$\chi_{1428}(659, \cdot)$$ n/a 432 2
1428.2.ba $$\chi_{1428}(271, \cdot)$$ n/a 288 2
1428.2.bd $$\chi_{1428}(341, \cdot)$$ 1428.2.bd.a 42 2
1428.2.bd.b 42
1428.2.be $$\chi_{1428}(611, \cdot)$$ n/a 560 2
1428.2.bg $$\chi_{1428}(101, \cdot)$$ 1428.2.bg.a 96 2
1428.2.bj $$\chi_{1428}(443, \cdot)$$ n/a 512 2
1428.2.bk $$\chi_{1428}(103, \cdot)$$ n/a 256 2
1428.2.bn $$\chi_{1428}(373, \cdot)$$ 1428.2.bn.a 4 2
1428.2.bn.b 44
1428.2.bo $$\chi_{1428}(253, \cdot)$$ 1428.2.bo.a 24 4
1428.2.bo.b 40
1428.2.bp $$\chi_{1428}(155, \cdot)$$ n/a 864 4
1428.2.bs $$\chi_{1428}(223, \cdot)$$ n/a 576 4
1428.2.bt $$\chi_{1428}(461, \cdot)$$ n/a 192 4
1428.2.bw $$\chi_{1428}(89, \cdot)$$ n/a 192 4
1428.2.by $$\chi_{1428}(115, \cdot)$$ n/a 576 4
1428.2.ca $$\chi_{1428}(191, \cdot)$$ n/a 1120 4
1428.2.cc $$\chi_{1428}(361, \cdot)$$ 1428.2.cc.a 8 4
1428.2.cc.b 16
1428.2.cc.c 72
1428.2.cg $$\chi_{1428}(97, \cdot)$$ n/a 192 8
1428.2.ch $$\chi_{1428}(29, \cdot)$$ n/a 288 8
1428.2.ci $$\chi_{1428}(211, \cdot)$$ n/a 864 8
1428.2.cj $$\chi_{1428}(167, \cdot)$$ n/a 2240 8
1428.2.co $$\chi_{1428}(25, \cdot)$$ n/a 192 8
1428.2.cp $$\chi_{1428}(179, \cdot)$$ n/a 2240 8
1428.2.cs $$\chi_{1428}(19, \cdot)$$ n/a 1152 8
1428.2.ct $$\chi_{1428}(185, \cdot)$$ n/a 384 8
1428.2.cw $$\chi_{1428}(131, \cdot)$$ n/a 4480 16
1428.2.cx $$\chi_{1428}(79, \cdot)$$ n/a 2304 16
1428.2.cy $$\chi_{1428}(65, \cdot)$$ n/a 768 16
1428.2.cz $$\chi_{1428}(61, \cdot)$$ n/a 384 16

"n/a" means that newforms for that character have not been added to the database yet

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(1428))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(1428)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(17))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(21))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(28))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(34))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(42))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(51))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(68))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(84))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(102))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(119))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(204))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(238))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(357))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(476))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(714))$$$$^{\oplus 2}$$